NEW YORK — Hostess has picked the maker of Little Debbie as the lead bidder for its Drake’s cakes.

According to documents filed in US Bankruptcy Court, McKee Foods has offered $27.5 million in cash for the cake brands, which include Devil Dogs, Funny Bones, and Yodels. The fate of Twinkies and other Hostess cakes is still being negotiated with other bidders.

Hostess also said United States Bakery agreed to pay $28.9 million for its remaining bread brands, which include Sweetheart, Eddy’s, Standish Farms, and Grandma Emilie’s. That offer includes four bakeries, 14 depots, and equipment.

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Earlier this month, Hostess picked Flowers Foods, which makes Tastykake and Nature’s Own and Bunny bread, as lead bidder for six of its major bread brands, including Wonder.

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The ‘‘stalking horse’’ bid by McKee Foods would set the floor for an auction process that lets competitors make better offers. A judge would have to approve the final sale, which Hostess said is scheduled to close no later than May 30.

McKee’s bid includes some equipment but not the Drake’s bakery in Wayne, N.J. A spokesman for Hostess, Tom Becker, said the company continues ‘‘to market all remaining assets.’’

McKee, of Collegedale, Tenn., makes a variety of snack cakes under the Little Debbie banner that compete with Hostess cakes at a lower price. For example, its Cloud Cakes resemble Twinkies and its Devil Cremes resemble Devil Dogs. A representative for McKee Foods, Mike Gloekler, said the company didn’t plan to scrap any brands.

He said McKee hoped to make Drake’s products at its plant in Stuarts Draft, Va., since Drake’s cakes are best known in the Northeast.

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Hostess has said previously that it needed to move quickly in selling brands to capitalize on the outpouring of nostalgia and media coverage prompted by its demise. The company repeated the sentiment in its court filing Monday, noting there is no advertising or marketing for Drake’s brands, which include Ring Dings and Yankee Doodles.

‘‘The longer Drake’s products stay off the shelves, the more likely it is that consumers will begin to use competitors’ products,’’ the filing said.

McKee generates about $1.1 billion in sales a year, with its Little Debbie cake division accounting for $800 million of that, according to the company. In recent years, McKee has seen its sales remain flat or fall.

Hostess Brands Inc., based in Irving, Texas, has been plagued by even greater problems. It said in November that it was shutting down its business and selling its breads and snack cakes, after years of management turmoil.